Apparatus and method for minimizing drift of a piezo-resistive pressure sensors due to progressive release of mechanical stress over time

ABSTRACT

An absolute piezo-resistive pressure sensor system and method employing multiple pressure sensing elements operating simultaneously to detect pressure. Both pressure sensing elements being subject to a common reference pressure within a sealed cavity. The first pressure sensing element detecting an offset voltage resulting from the progressive release of mechanical stress at an assembly interface between the sensing element and a base plate on which the sensing elements are assembled. Electronic circuitry compensates the pressure measured by the second pressure sensing element based on the offset voltage detected by the first pressure sensing element.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to an absolute piezo-resistive pressuresensor or transducer. More particularly, the invention relates to anapparatus and method for minimizing drift of an absolute piezo-resistivepressure sensor due to the progressive release of mechanical stress overtime.

2. Description of Related Art

Absolute micro pressure sensors have a relatively thin silicondeflectable membrane that mechanically deflects under pressure. Themechanical deflection of the membrane is correlated to a pressure beingmeasured on one side of the membrane. In order to measure an absolutepressure, the opposite side of the membrane is exposed to asubstantially constant pressure created at the time of manufacture by ahermetically sealed cavity.

FIG. 1 is a cross-sectional view of a prior art absolute piezo-resistivepressure sensor. Such a piezo-resistive sensor measures the mechanicaldeflection of a membrane or diaphragm by measuring a change inelectrical resistance of a piezo-resistive film deposited or diffused onthe membrane. A silicon wafer or die 10 is etched to form a cavity 25closed at one end by a relatively thin deflectable membrane or diaphragm40. One side of the membrane 40 is exposed to a pressure being measured(Pmeasured) within the cavity 25, while an opposite side of the membrane40 is subject to an absolute or substantially constant referencepressure (Pref) within a hermetically sealed chamber 35 filled with gas.A piezo-resistive material or film 30 is deposited or diffused on thesurface of the membrane within the hermetically sealed chamber 35. Thesilicon wafer 10 is assembled to a glass base plate 5 so that themembrane 40 is substantially aligned with an opening or hole 20 definedin the base plate 5.

Anodic bonding is a well known method for hermetically and permanentlybonding silicon to glass without the use of adhesives. Silicon and glasscomponents are heated to a temperature typically in the range of betweenapproximately 300° C.-approximately 500° C., depending on the glasstype. At such temperatures, alkali metal ions in the glass becomemobile. A relatively high voltage (e.g., approximately 250V-approximately 1000 V) is applied across the components as they arebrought proximate or in contact with one another causing the alkalications to migrate from the interface resulting in a depletion layerwith relatively high electric field strength. The resultingelectrostatic attraction brings the silicon and glass components intointimate contact with one another. Further current flow of the oxygenanions from the glass to the silicon results in an anodic reaction andhence a permanent chemical bond at the interface between the twocomponents without the need for a bonding interface material oradhesive.

FIG. 3 is a side view of the sensing element of FIG. 1 assembled to theglass base plate using an alternative eutectic solder alloy (e.g.,60SN40Pb solder alloy). This process requires the bonding surfaces to beplated with noble metals in layers preferably of only fractions of amicron thick. The mechanical stress resulting at the assembly interfaceand therefore at the deflectable membrane occurs over time due to agingeffects regardless of the type of assembly method or process used.Another factor contributing to the overall mechanical stress resultsfrom temperature variations if the coefficient of thermal expansion ofthe sensing element and base plate (substrate) are not matched.

In order to protect its electronic circuitry against malfunction whenmonitoring pressure within certain environments the piezo-resistivepressure transducer or sensor shown in FIG. 1 is encapsulatd in ahermetically sealed packaging or enclosure 50 depicted in FIG. 2. EPPatent No.1 184 351 discloses a method for brazing two glass componentstogether in order to form leak tight container for encapsulatingelectronic components such as a pressure transducer implanted in a humanbody. Enclosure 50 formed by cover 55 and base plate 5 are brazedtogether forming a hermetic seal. The enclosure is preferably made ofglass and filled with a gas or fluid at a substantially constantpressure P1. Most preferably, glass enclosure 50 is filled with an inertgas such as helium or argon in order to prevent or minimizeoxidation/aging of electronic circuitry 65 disposed therein. Anotherfactor in the selection of the gas or fluid for filling enclosure 50, isthat it preferably be compliant with a leak tester used for testing theimplant hermeticity after encapsulation. The capsule or packaging isplaced in a hermetically sealed helium chamber subject to asubstantially constant pressure preferably in the range of approximately100 mbar-approximately 1000 mbar to detect any helium molecules escapingor leaking from the capsule.

Over time the pressure sensor measurement response of a conventionalabsolute piezo-resistive pressure sensor will undesirably drift due tounwanted mechanical stress. It is therefore desirable to develop animproved absolute piezo-resistive pressure sensor that calibrates andthen compensates for pressure sensor drift over time due to mechanicalstress.

SUMMARY OF THE INVENTION

An aspect of the present invention is directed to an absolutepiezo-resistive pressure sensor that compensates for long term driftassociated with mechanical stress detected by a pressure sensor elementseparate from the pressure sensor element used to monitor the pressurebeing measured.

Another aspect of the present invention relates to an absolutepiezo-resistive pressure sensor system and method employing multiplepressure sensing elements operating simultaneously to detect pressure.Both pressure sensing elements being subject to a common referencepressure within a sealed cavity. The first pressure sensing elementdetecting an offset voltage resulting from the progressive release ofmechanical stress at an assembly interface between the sensing elementand a base plate on which the sensing elements are assembled. Electroniccircuitry compensates the pressure measured by the second pressuresensing element based on the offset voltage detected by the firstpressure sensing element.

Yet another aspect of the present invention is directed to an absolutepiezo-resistive pressure sensor system including a single wafer havingrespective first and second cavities etched therein forming respectivefirst and second deflectable membranes serving as respective first andsecond pressure sensing elements. The first deflectable membrane has anaperture defined therethrough, while the second deflectable membranedoes not. A first surface of each of the first and second deflectablemembranes is exposed to a pressure within the respective first andsecond cavities. An opposing second surface of each of the first andsecond deflectable membranes is enclosed in a common hermetically sealedchamber formed by a cover assembled to the single wafer, wherein apressure within the chamber is substantially constant. A piezo-resistivematerial is assembled to the opposing second surface of each of thefirst and second deflectable membranes subject to the same pressurewithin the sealed chamber. The wafer is assembled to a base plate havinga hole defined therein such that the second pressure sensing element issubstantially aligned with the hole. The present invention also relatesto a method for using such a system wherein simultaneously whiledetecting using the second pressure sensing element a pressure in thesecond cavity, a measured offset voltage detected by the first pressuresensing element due to mechanical stress release at an assemblyinterface between the wafer and the base plate is calibrated. Electroniccircuitry then compensates the pressure in the second cavity detected bythe second pressure sensing element based on the offset voltage ascalibrated by the first pressure sensing element.

Still another aspect of the present invention relates to an absolutepiezo-resistive pressure sensor system including two wafers. A firstwafer has a single cavity etched therein forming a first deflectablemembrane serving as a first pressure sensing element. The firstdeflectable membrane has an aperture defined therethrough, a firstsurface exposed to a pressure within the single cavity etched in thefirst wafer, and an opposing second surface. A second wafer has a singlecavity etched therein forming a second deflectable membrane serving as asecond pressure sensing element. The second deflectable membrane doesnot have an aperture defined therein; but does have a first surfaceexposed to a pressure within the single cavity etched in the secondwafer and an opposing second surface. Opposing second surfaces of thefirst and second deflectable membranes are enclosed in a commonhermetically sealed chamber formed by a cover enclosing the two siliconwafers, wherein a pressure within the chamber is substantially constant.A common piezo-resistive material is assembled to each of the opposingsecond surfaces of the first and second deflectable membranes subject tothe same pressure within the sealed chamber. A base plate having asingle hole define therein; the first and second wafers being assembledto the base plate with the hole substantially aligned with the secondpressure sensing element. The first and second wafers are fabricatedusing identical manufacturing steps, and the first and second pressuresensing elements are assembled using identical mounting steps. Also anaspect of the present invention is the method for using such a system bysimultaneously while detecting using the second pressure sensing elementa pressure in the second cavity, calibrating a measured offset voltagedetected by the first pressure sensing element due to mechanical stressrelease at an assembly interface between the two wafers and the baseplate. Thereafter, electronic circuitry is sued to compensate thepressure in the second cavity detected by the second pressure sensingelement based on the offset voltage as calibrated by the first pressuresensing element.

BRIEF DESCRIPTION OF THE DRAWING

The foregoing and ether features of the present invention will be morereadily apparent from the following detailed description and drawings ofillustrative embodiments of the invention wherein like reference numbersrefer to similar elements throughout the several views and in which:

FIG. 1 is a cross-sectional view of a prior art absolute piezo-resistivepressure sensor;

FIG. 2 is a cross-sectional view of a prior art hermetically sealedglass enclosure encapsulating the absolute piezo-resistive pressuresensor of FIG. 1;

FIG. 3 is a side view assembly of the absolute piezo-resistive pressuresensor of FIG. 1 mounted to the base plate using a eutectic solderalloy;

FIG. 4 is a cross-sectional view of a modified absolute piezo-resistivepressure sensor in accordance with the present invention fabricated froma single silicon wafer;

FIG. 5 is a cross-sectional view of the present inventive modifiedabsolute piezo-resistive pressure sensor of FIG. 4 encapsulated in ahermetically sealed glass enclosure; and

FIG. 6 is a cross-sectional view of a modified absolute piezo-resistivepressure sensor in accordance with the present invention fabricatedusing two silicon wafers.

DETAILED DESCRIPTION OF THE INVENTION

The accuracy or consistency of the pressure sensor measurements orreadings depends on certain properties, characteristics or conditionsideally remaining substantially unchanged. Unfortunately, it isimpossible to ideally maintain such constant conditions. Therefore, overtime conventional absolute piezo-resistive pressure sensors ortransducers always, but undesirably, exhibit a drift in pressure sensormeasurements or readings.

Several factors have been recognized that contribute toward progressivedrift in pressure sensor readings over time. During assembly of thesilicon sensing element to the glass base plate (substrate), forexample, using an anodic bonding process wherein the silicon sensingelement is heated and an electrical field is applied thereto, residualmechanical stress may be trapped within the silicon sensing elementstructure.

Another identified contributing factor to mechanical stress occurs whenthe anodically bonded glass and silicon components have different orunmatched coefficients of thermal expansion (CTE). Thus, at the assemblyinterface between the two components, any change in temperature willeffect the materials differently subjecting the silicon sensing elementstructure to mechanical stress. The greater the difference in CTEbetween the two components at the bonding interface the greater themechanical stress imposed on the sensing element structure withvariation in temperature.

Over time any trapped mechanical stress in the silicon sensing elementstructure dissipates thereby varying the mechanical deflection of thedeflectable sensor membrane and, in turn, the electrical resistance ofthe piezo-resistive material deposited or diffused to the membrane, asdenoted by the dashed line in FIG. 2. Such a change in electricalresistance will result in a drift of the pressure sensor response thatundesirably effects the accuracy of the measurements or readings overtime.

The present inventive system and method calibrates and then compensatesfor variation in mechanical deflection of the sensor membraneattributable to the progressive release of mechanical stress over time.To achieve this goal, the present inventive system employs two pressuresensing elements. A first pressure sensing element calibrates the impactof the progressive release of mechanical stress on the deflectablemembrane while a second pressure sensing element is used to detect apressure to be measured while compensating for the drift imposed by theprogressive release of mechanical stress as calibrated by the firstpressure sensing element.

FIG. 4 is a cross-sectional view of an exemplary absolutepiezo-resistive pressure sensor system 400 in accordance with thepresent invention. System 400 is preferably fabricated employing asingle silicon wafer or die 405 having two cavities 410, 415 etchedtherein forming two respective deflectable membranes or diaphragms 420,425 serving as two pressure sensing elements. One surface of the firstand second deflectable membranes 420, 425 is exposed to a pressurewithin the respective first and second cavities 410, 415, while anopposing surface of the first and second deflectable membranes 420, 425is enclosed in a common hermetically sealed chamber 430 at asubstantially constant pressure (Pref) formed by a glass cover 435bonded to the single silicon wafer or die 405. A piezo-resistivematerial 470 is deposited or diffused to that surface of the first andsecond deflectable membranes 420, 425 subject to the same pressure(Pref) within the sealed chamber 430. The silicon wafer 405 is, in turn,assembled (preferably anodically bonded, to a glass base plate 440 witha single hole or opening 445 defined therein and substantially alignedwith the second sensing element (i.e., second cavity 415 and seconddeflectable membrane 425). Preferably, the hole or opening 445 is in therange between approximately 0.5 mm-approximately 2.5 mm. The firstdeflectable membrane 420 has an aperture 450 defined therethrough(preferably between approximately 0.05 mm-approximately 0.1 mm), whilethe second deflectable membrane 425 does not. The silicon wafer 405forming the two pressure sensing elements is itself encapsulated in ahermetically sealed chamber or packaging 460 formed by cover 455 andbase plate 440 in accordance with known bonding or brazing techniquessuch as that disclosed in EP 1 184 351, assigned to the same company asthat of the present invention and herein incorporated by reference inits entirety. Chamber 460 is preferably filled with a gas at asubstantially constant pressure (P1), preferably an inert gas such ashelium.

As an alternative to fabricating the present inventive system using asingle silicon wafer having two cavities defined therein forming twodeflectable sensor membranes, two silicon wafers may be used to formseparate sensing elements (as shown in FIG. 6), so long as both sensingelements are fabricated following identical manufacturing steps andthereafter simultaneously assembled to the glass base plate (substrate)following identical mounting steps. Applying the same fabrication andassembly steps insures that the drift from the progressive release ofmechanical stress as experienced by the two pressure sensing elementswill be the same. This two silicon wafer fabrication embodiment as shownin FIG. 6 can also be encapsulated by a cover 455 to form a chamber 460(similar to that shown in FIG. 5 for the single wafer fabrication).

Due to the aperture 450 defined in the first deflectable membrane 420,both sides of the first deflectable membrane 420 are exposed to the samepressure, e.g., the substantially constant pressure in chamber 430(Pref). Since chamber 430 is hermetically sealed the pressure (Pref)will remain substantially unchanged. Accordingly, any mechanicaldeflection of the first deflectable membrane 420 and change inresistance of the piezo-resistive film is deemed attributable to theprogressive release of mechanical stress occurring at the assemblyinterface of the first sensing element to the glass base plate 440 (asdenoted by the dashed lines in FIGS. 5 & 6). This variation inresistance is translated by the associated electronic circuitry 465(signal processing and other electronic circuitry) into an electricalsignal representing the current drift due to mechanical stress.

Accordingly, in operation, the pressure of both pressure sensingelements is detected simultaneously. Specifically, the piezo-resistiveelements of each pressure sensing element are typically connected as aWheatstone bridge to measure detect changes in resistance. TheWheatstone bridge passes a current through the sensors and measures theoutput voltage. When the resistance changes, less current passes throughthe pressure sensor. The Wheatstone bridge detects this change inresistance whose output is proportional to a change in pressure. Themechanical deflection of the first membrane 425 resulting from theprogressive release of mechanical stress is thus calibrated as (offsetvoltage (Voffset)) by the first pressure sensing element, while thesecond pressure sensing element and associated membrane 425simultaneously detects a pressure to be measured within cavity 415. Thesensed pressure detected by the second pressure sensing element,however, is compensated or offset by the electronic circuitry 465 tocorrect for the mechanical deflection of the first membrane 425(Voffset) detected or calibrated by the first pressure sensing elementresulting from the progressive release of mechanical stress. Thiscorrected pressure sensor measurement or reading therefore has animproved pressure reading response.

It should be noted that the present inventive absolute piezo-resistivepressure sensor has been described as being for a medical purpose andimplanted in the body. The scope of the present invention is equallysuited for non-medical as well as medical applications outside the body.Nothing in this description is intended to limit the scope of thepresent invention to a particular application or use.

Thus, while there have been shown, described, and pointed outfundamental novel features of the invention as applied to a preferredembodiment thereof, it will be understood that various omissions,substitutions, and changes in the form and details of the devicesillustrated, and in their operation, may be made by those skilled in theart without departing from the spirit and scope of the invention. Forexample, it is expressly intended that all combinations of thoseelements and/or steps that perform substantially the same function, insubstantially the same way, to achieve the same results be within thescope of the invention. Substitutions of elements from one describedembodiment to another are also fully intended and contemplated. It isalso to be understood that the drawings are not necessarily drawn toscale, but that they are merely conceptual in nature. It is theintention, therefore, to be limited only as indicated by the scope ofthe claims appended hereto.

Every issued patent, pending patent application, publication, journalarticle, book or any other reference cited herein is each incorporatedby reference in their entirety.

1. An absolute piezo-resistive pressure sensor system comprising: asingle wafer having respective first and second cavities etched thereinforming respective first and second deflectable membranes serving asrespective first and second pressure sensing elements; the firstdeflectable membrane having an aperture defined therethrough, while thesecond deflectable membrane does not; a first surface of each of thefirst and second deflectable membranes being exposed to a pressurewithin the respective first and second cavities; an opposing secondsurface of each of the first and second deflectable membranes beingenclosed in a common hermetically sealed chamber formed by a coverassembled to the single wafer, wherein a pressure within the chamber issubstantially constant; a piezo-resistive material is assembled to theopposing second surface of each of the first and second deflectablemembranes subject to the same pressure within the sealed chamber; and abase plate having a single hole define therein; the wafer beingassembled to the base plate with the hole substantially aligned with thesecond pressure sensing element.
 2. The system in accordance with claim1, wherein the wafer is made of silicon and the base plate is made ofglass.
 3. The system in accordance with claim 1, the aperture definedtherethrough the first deflectable membrane is between approximately0.05 mm-approximately 0.1 mm.
 4. The system in accordance with claim 1,further comprising a cover assembled to the base plate to form apackaging that encapsulates the wafer forming the two pressure sensingelements in a hermetically sealed chamber at a substantially constantpressure.
 5. The system in accordance with claim 1, further comprisingelectronic circuitry for: (i) simultaneously while detecting using thesecond pressure sensing element a pressure in the second cavity,calibrating a measured offset voltage detected by the first pressuresensing element due to mechanical stress release at an assemblyinterface between the wafer and the base plate; and (ii) compensatingthe pressure in the second cavity detected by the second pressuresensing element based on the offset voltage as calibrated by the firstpressure sensing element.
 6. The system in accordance with claim 1,wherein a material used to fabricate the single wafer has a differentcoefficient of thermal expansion than a material used to fabricate thebase plate.
 7. An absolute piezo-resistive pressure sensor systemcomprising: a first wafer, having a single cavity etched therein forminga first deflectable membrane serving as a first pressure sensingelement; the first deflectable membrane having an aperture definedtherethrough; the first deflectable membrane having a first surfaceexposed to a pressure within the single cavity etched in the first waferand an opposing second surface; a second wafer having a single cavityetched therein forming a second deflectable membrane serving as a secondpressure sensing element; the second deflectable membrane not having anaperture defined therein; the second deflectable membrane having a firstsurface exposed to a pressure within the single cavity etched in thesecond wafer and an opposing second surface; the opposing secondsurfaces of the first and second deflectable membranes being enclosed ina common hermetically sealed chamber formed by a cover enclosing the twosilicon wafers, wherein a pressure within the chamber is substantiallyconstant; a common piezo-resistive material is assembled to each of theopposing second surfaces of the first and second deflectable membranessubject to the same pressure within the sealed chamber; and a base platehaving a single hole define therein; the first and second wafers beingassembled to the base plate with the hole substantially aligned with thesecond pressure sensing element; wherein the first and second wafers arefabricated using identical manufacturing steps, and the first and secondpressure sensing elements are assembled using identical mounting steps.8. The system in accordance with claim 7, wherein the first and secondwafers are made of silicon, and the base plate is made of glass.
 9. Thesystem in accordance with claim 7, the aperture defined therethrough thefirst deflectable membrane is between approximately 0.05mm-approximately 0.1 mm.
 10. The system in accordance with claim 7,further comprising a cover assembled to the base plate to form apackaging that encapsulates the two wafers forming the two pressuresensing elements in a hermetically sealed chamber at a substantiallyconstant pressure.
 11. The system in accordance with claim 7, furthercomprising electronic circuitry for: (i) simultaneously while detectingusing the second pressure sensing element a pressure in the secondcavity, calibrating a measured offset voltage detected by the firstpressure sensing element due to mechanical stress release at an assemblyinterface between the two wafers and the base plate; and (ii)compensating the pressure in the second cavity detected by the secondpressure sensing element based on the offset voltage as calibrated bythe first pressure sensing element.
 12. The system in accordance withclaim 7, wherein a material used to fabricate the two wafers has adifferent coefficient of thermal expansion than a material used tofabricate the base plate.
 13. A method for operating an absolutepiezo-resistive pressure sensor system including a single wafer havingrespective first and second cavities etched therein forming respectivefirst and second deflectable membranes serving as respective first andsecond pressure sensing element; the first deflectable membrane havingan aperture defined therethrough, while the second deflectable membranedoes not; a first surface of each of the first and second deflectablemembranes being exposed to a pressure within the respective first andsecond cavities; an opposing second surface of each of the first andsecond deflectable membranes being enclosed in a common hermeticallysealed chamber formed by a cover assembled to the single wafer, whereina pressure within the chamber is substantially constant; apiezo-resistive material is assembled to the opposing second surface ofeach of the first and second deflectable membranes subject to the samepressure within the sealed chamber; a base plate having a single holedefine therein; the silicon wafer being assembled to the base plate withthe hole substantially aligned with the second pressure sensing element,the method comprising the steps of: simultaneously while detecting usingthe second pressure sensing element a pressure in the second cavity,calibrating a measured offset voltage detected by the first pressuresensing element due to mechanical stress release at an assemblyinterface between the wafer and the base plate; and compensating usingelectronic circuitry the pressure in the second cavity detected by thesecond pressure sensing element based on the offset voltage ascalibrated by the first pressure sensing element.
 14. The method inaccordance with claim 13, wherein the single wafer is made of siliconand the base plate is made of glass.
 15. The method in accordance withclaim 13, the aperture defined therethrough the first deflectablemembrane is between approximately 0.05 mm-approximately 0.1 mm.
 16. Themethod in accordance with claim 13, further comprising a cover assembledto the base plate to form a packaging that encapsulates the single waferforming the two pressure sensing elements in a hermetically sealedchamber at a substantially constant pressure.
 17. The method inaccordance with claim 13, wherein a material used to fabricate thesingle wafer has a different coefficient of thermal expansion than amaterial used to fabricate the base plate.
 18. A method for operating anabsolute piezo-resistive pressure sensor system including a first wafer,having a single cavity etched therein forming a first deflectablemembrane serving as a first pressure sensing element; the firstdeflectable membrane having an aperture defined therethrough; the firstdeflectable membrane having a first surface exposed to a pressure withinthe single cavity etched in the first wafer and an opposing secondsurface; a second wafer having a single cavity etched therein forming asecond deflectable membrane serving as a second pressure sensingelement; the second deflectable membrane not having an aperture definedtherein; the second deflectable membrane having a first surface exposedto a pressure within the single cavity etched in the second wafer and anopposing second surface; the opposing second surfaces of the first andsecond deflectable membranes being enclosed in a common hermeticallysealed chamber formed by a cover enclosing the two wafers, wherein apressure within the chamber is substantially constant; a commonpiezo-resistive material is assembled to each of the opposing secondsurfaces of the first and second deflectable membranes subject to thesame pressure within the sealed chamber; and a base plate having asingle hole define therein; the first and second wafers being assembledto the base plate with the hole substantially aligned with the secondpressure sensing element; the first and second wafers being fabricatedusing identical manufacturing steps, and the first and second pressuresensing elements being assembled using identical mounting steps; themethod comprising the steps of: simultaneously while detecting using thesecond pressure sensing element a pressure in the second cavity,calibrating a measured offset voltage detected by the first pressuresensing element due to mechanical stress release at an assemblyinterface between the two wafers and the base plate; and compensatingusing electronic circuitry the pressure in the second cavity detected bythe second pressure sensing element based on the offset voltage ascalibrated by the first pressure sensing element.
 19. The method inaccordance with claim 18, wherein the first and second wafers are madeof silicon, and the base plate is made of glass.
 20. The method inaccordance with claim 18, the aperture defined therethrough the firstdeflectable membrane is between approximately 0.05 mm-approximately 0.1mm.
 21. The method in accordance with claim 18, further comprising acover assembled to the base plate to form a packaging that encapsulatesthe two wafers forming the two pressure sensing elements in ahermetically sealed chamber at a substantially constant pressure. 22.The method in accordance with claim 18, wherein a material used tofabricate the two wafers has a different coefficient of thermalexpansion than a material used to fabricate the base plate.
 23. Themethod in accordance with claim 18, wherein a material used to fabricatethe two wafers has a different coefficient of thermal expansion than amaterial used to fabricate the base plate.